One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Hidden Fibonacci numbers, a new shape and the search for a grand unified theory of mathematics are among our choices for most ...

The Poincaré conjecture can be understood by analogy with the case in two dimensions. A two-dimensional space, or surface, is like a bubble made from an infinitely thin film of soap. If the bubble is ...

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics. In mathematics, a simple problem is often not what it seems. Earlier this ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...